Why cant I see the loop cut line on one side of the mirrored shape
There are two options to display the result of the modifier in edit mode:

(form the Blender Manual)

Box
Displays the modified geometry in edit mode, as well as the original geometry which you can edit.
Triangle
When enabled, the final modified geometry will be shown in edit mode and can be edited directly.

Enabling the triangle will allow you to &quot;adjust edit cage to modifier result&quot; :